Coupled, multi-strain epidemic models of mutating pathogens

TL;DR

This paper develops coupled multi-strain epidemic models to understand how mutant pathogen strains emerge and coexist, revealing that reproduction numbers are unaffected by mutation rates and that coupling promotes strain coexistence.

Contribution

The paper introduces a general class of coupled multi-strain epidemic models and analyzes their properties, including the independence of reproduction numbers from mutation rates and the promotion of strain coexistence.

Findings

Reproduction number of each strain is independent of mutation rates.

Coupling promotes coexistence of multiple strains.

The most reproductive strain is not always the most prevalent.

Abstract

We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains --- even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning.